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arXiv:cond-mat/9807056 · Physical Review Letters

Comment on “Phase and Phase Diffusion of a Split Bose-Einstein Condensate”

A. J. Leggett, Fernando Sols

Published Aug 10, 1998• 63 citations
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Abstract

Recently Javanainen and Wilkens [Phys. Rev. Lett. 78, 4675 (1997)] have analysed an experiment in which an interacting Bose condensate, after being allowed to form in a single potential well, is "cut" by splitting the well adiabatically with a very high potential barrier, and estimate the rate at which, following the cut, the two halves of the condensate lose the "memory" of their relative phase. We argue that, by neglecting the effect of interactions in the initial state before the separation, they have overestimated the rate of phase randomization by a numerical factor which grows with the interaction strength and with the slowness of the separation process.

DOI
10.1103/physrevlett.81.1344

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Recently Javanainen and Wilkens [Phys. Rev. Lett. 78, 4675 (1997)] have analysed an experiment in which an interacting Bose condensate, after being allowed to form in a single potential well, is "cut" by splitting the well adiabatically with a very high potential barrier, and estimate the rate at which, following the cut, the two halves of the condensate lose the "memory" of their relative phase. We argue that, by neglecting the effect of interactions in the initial state before the separation, they have overestimated the rate of phase randomization by a numerical factor which grows with the interaction strength and with the slowness of the separation process.
We study the quantum dynamics of a Bose–Einstein condensate trapped in a double-well potential with a rising interwell barrier. We analytically find the characteristic timescales of the splitting process and compare our results with numerical analyses available in the literature. In the first stage of the dynamics, the relative phase of the two condensates evolves adiabatically. At a critical time t ad , small-amplitude phase fluctuations around the average trajectory increase exponentially fast, signalling the breakdown of adiabaticity. After this stage, it is still not possible to neglect the tunnelling exchange between the two wells. We find highly non-trivial dependences of the dephasing time on t ad and on the ramping time of the interwell barrier.
We study the collisional loss of atom-molecule coherence after coherently dissociating a small fraction of a molecular Bose-Einstein condensate into atoms. The obtained nnn-atoms states are two-atom (SU(1,1)) coherent states with number variance Δn∝nΔn\propto nΔn∝n compared to Δn∝nΔn\propto \sqrt{n}Δn∝n​ for the spin (SU(2)) coherent states formed by coherent splitting of an atomic condensate. Consequently, the Lorentzian atom-molecule phase-diffusion is faster than the Gaussian phase-diffusion between separated atomic condensates, by a n\sqrt{n}n​ factor.
Motivated by a recent experiment [Chikkatur et al., Science, 296, 2193 (2002)] on the merging of atomic condensates, we investigate how two independent condensates with random initial phases can develop a unique relative phase when we move them together. In the adiabatic limit, the uniting of independent condensates can be understood from the eigenstate evolution of the governing Hamiltonian, which maps degenerate states (corresponding to fragmented condensates) to a single state (corresponding to a united condensate). In the nonadiabatic limit corresponding to the practical experimental configurations, we give an explanation on why we can still obtain a large condensate fraction with a unique relative phase. Detailed numerical simulations are then performed for the nonadiabatic merging of the condensates, which confirm our explanation and qualitative estimation. The results may have interesting implications for realizing a continuous atom laser based on the merging of condensates.
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